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Suppose a dealer has a local monopoly in selling good X. It pays w to the manufacturer for each unit of X that it sells, and charges each customer p. The demand curve that the dealer faces is best described by the linear function Q-30-p, where the price is in units of thousands of dollars. a. What is the profit-maximizing price for the dealer to set? At this price, how many units of X will the dealer sell and what will the dealers profit be? Now let us think about how the situation looks from the manufacturers point of view. If it charges w per unit of X to its dealer, calculate how many units of X the dealer wil buy from the manufacturer. In other words, what is the demand curve facing the manufacturer? Suppose that it costs the manufacturer $5,000 to produce each unit. What is the profit-maximizing choice of w? What will the manufacturers profits be? What price p will the dealer set and what profit will the dealer earn at the manufacturers profit-maximizing choice of price w? Graph your answer

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A dealer has a local monopoly in selling good X. It pays w to the manufacturer for each unit of X that it sells, and charges each customer p. So w<p

The demand curve that the dealer faces is best described by the linear function Q = 30 ? p, where the price is in units of thousands of dollars. TR = 30Q - Q2 and MR = 30 - 2Q

a. The profit-maximizing price for the dealer to set is given as

MR = MC

30 - 2Q = w

Q = 15 - 0.5w

Price = 30 - Q or 15 + 0.5w

At this price, the dealer sells 15 - 0.5w units of X. Dealer’s profit will be (P -MC)*Q = (15 + 0.5w - w)(15 - 0.5w) = (15 - 0.5w)2

b. Now let us think about how the situation looks from the manufacturer’s point of view. If it charges w per unit of X to its dealer, calculate how many units of X the dealer will buy from the manufacturer. In other words, Demand is

Q = 15 - 0.5w

or

w = 30 - 2Q

MR = 30 - 4Q

MC = 5

MR = MC.

30 - 4Q = 5

Q = 6.25

w = 18.5 (or 18500)

P = 24.25

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